U.S. patent number 7,333,891 [Application Number 11/400,536] was granted by the patent office on 2008-02-19 for correction of cross-component induction measurements for misalignment using comparison of the xy formation response.
This patent grant is currently assigned to Baker Hughes Incorporated. Invention is credited to Bill H. Corley, Luis M. Pelegri, Michael B. Rabinovich, Leonty A. Tabarovsky.
United States Patent |
7,333,891 |
Rabinovich , et al. |
February 19, 2008 |
Correction of cross-component induction measurements for
misalignment using comparison of the XY formation response
Abstract
Measurements are made with a multicomponent logging tool in an
earth formation. The measurements are inverted without using a
selected cross-component measurement. The model is then used to
predict the value of the selected cross-component. A misalignment
angle of the tool is estimated from the predicted and actual values
of the selected cross-component.
Inventors: |
Rabinovich; Michael B.
(Houston, TX), Tabarovsky; Leonty A. (Cypress, TX),
Corley; Bill H. (Conroe, TX), Pelegri; Luis M. (Humble,
TX) |
Assignee: |
Baker Hughes Incorporated
(Houston, TX)
|
Family
ID: |
38576484 |
Appl.
No.: |
11/400,536 |
Filed: |
April 6, 2006 |
Prior Publication Data
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|
|
Document
Identifier |
Publication Date |
|
US 20070239360 A1 |
Oct 11, 2007 |
|
Current U.S.
Class: |
702/7 |
Current CPC
Class: |
G01V
3/28 (20130101) |
Current International
Class: |
G01V
3/28 (20060101) |
Field of
Search: |
;702/7,9,10,11,12,13 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
Other References
Moran et al.; Basic Theory of Induction Logging and Application to
Study of Two-Coil Sondes, Society of Exploration Geophysicists,
vol. 27, No. 6, Dec. 1962, pp. 829-858. cited by other.
|
Primary Examiner: McElheny, Jr.; Donald E
Attorney, Agent or Firm: Madan, Mossman & Sriram,
P.C.
Claims
What is claimed is:
1. A method of estimating a parameter of interest of an earth
formation, the method comprising: (a) conveying a logging tool into
a borehole in the earth formation; (b) obtaining a plurality of
multi-component resistivity measurements using the logging tool;
(c) inverting the multi-component resistivity measurements without
using a particular cross-component to give a resistivity model at a
plurality of depths; (d) using the resistivity model to provide a
simulated value of the particular cross-component; and (e) using
the simulated value of the particular cross-component and an actual
value of the particular cross-component for estimating a
misalignment angle in the logging tool.
2. The method of claim 1 wherein inverting the multi-component
measurements further comprises using a search technique.
3. The method of claim 1 further comprising obtaining multi-array
induction measurements and using the multi-array induction
measurements in the inversion.
4. The method of claim 1 wherein inverting the multi-component
measurements further comprises: (i) using a first subset of the
measurements to estimate a horizontal resistivity of the formation,
and (ii) using the estimated horizontal resistivity and another
subset of the measurements to estimate a vertical resistivity of
the earth formation.
5. The method of claim 1 wherein inverting the multi-component
measurements further comprises using a separation of modes.
6. The method of claim 1 wherein the particular cross-component is
selected from (i) an XY component, and (ii) an XZ component.
7. The method of claim 1 wherein determining the misalignment angle
further comprises using an average value of the particular
cross-component and an average simulated value of the particular
cross-component.
8. The method of claim 1 further comprising using the misalignment
angle and the multi-component measurements to estimate the
parameter of interest of the earth formation.
9. The method of claim 8 wherein the parameter of interest is at
least one of (i) a horizontal conductivity, (ii) a vertical
conductivity, (iii) a horizontal resistivity, (iv) a vertical
resistivity, (v) a relative dip angle, (vi) a strike angle, (vii) a
sand fraction, (viii) a shale fraction, and (ix) a water
saturation.
10. An apparatus for estimating a parameter of interest of an earth
formation, the apparatus comprising: (a) a logging tool conveyed
into a borehole in the earth formation which obtains a plurality of
multi-component resistivity measurements; and (b) a processor
which: (A) inverts the multi-component resistivity measurements
without using a particular cross-component to give a resistivity
model at a plurality of depths; (B) uses the resistivity model to
provide a simulated value of the particular cross-component; and
(C) uses the simulated value of the particular cross-component and
an actual value of the particular cross-component to estimate a
misalignment angle in the logging tool.
11. The apparatus of claim 10 wherein the processor inverts the
multi-component measurements using a search technique.
12. The apparatus of claim 10 wherein the processor inverts the
multi-component measurements using: (i) a first subset of the
measurements to estimate a horizontal resistivity of the formation,
and (ii) the estimated horizontal resistivity and another subset of
the measurements to estimate a vertical resistivity of the earth
formation.
13. The apparatus of claim 10 wherein the processor inverts the
multi-component measurements by using a separation of modes.
14. The apparatus of claim 10 wherein the particular
cross-component is selected from (i) an XY component, and (ii) an
XZ component.
15. The apparatus of claim 10 wherein the processor estimates the
misalignment using an average value of the particular
cross-component and an average simulated value of the particular
cross-component.
16. The apparatus of claim 10 wherein the processor further uses
the estimated misalignment angle and the multi-component
measurements to estimate the parameter of interest of the earth
formation.
17. The apparatus of claim 16 wherein the parameter of interest is
at least one of (i) a horizontal conductivity, (ii) a vertical
conductivity, (iii) a horizontal resistivity, (iv) a vertical
resistivity, (v) a relative dip angle, (vi) a strike angle, (vii) a
sand fraction, (viii) a shale fraction, and (ix) a water
saturation.
18. The apparatus of claim 10 further comprising a wireline which
conveys the logging tool into the borehole.
19. The apparatus of claim 18 further comprising a motor which
rotates the logging tool to the plurality of rotational angles.
20. The apparatus of 10 wherein the logging tool is part of a
bottomhole assembly (BHA) conveyed into the borehole on a drilling
tubular.
21. A computer readable medium used with an apparatus for
evaluating an earth formation, the apparatus comprising: (a) a
logging tool conveyed into a borehole in the earth formation which
obtains a plurality of multi-component resistivity measurements;
the medium comprising instructions which enable a processor to (b)
invert the multi-component resistivity measurements without using a
particular cross-component to give a resistivity model at a
plurality of depths; (c) use the resistivity model to provide a
simulated value of the particular cross-component; and (d) estimate
a misalignment angle in the logging tool by using the simulated
value of the particular cross-component and an actual value of the
particular cross-component.
22. The medium of claim 20 further comprising at least one of (i) a
ROM, (ii) an EPROM, (iii) an EAROMs, (iv) a flash memory, and (v)
an Optical disk.
Description
CROSS-REFERENCES TO RELATED APPLICATIONS
This application is related to U.S. patent application Ser. No.
11/398,838 to Rabinovich et al., filed Apr. 6, 2006 and U.S. patent
application Ser. No. 11/400,097 to Rabinovich et al., filed Apr. 6,
2006.
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention is related to the field of apparatus design
in the field of oil exploration. In particular, the present
invention describes a method for calibrating multicomponent logging
devices used for detecting the presence of oil in boreholes
penetrating a geological formation.
2. Description of the Related Art
Electromagnetic induction resistivity well logging instruments are
well known in the art. Electromagnetic induction resistivity well
logging instruments are used to determine the electrical
conductivity, and its converse, resistivity, of earth formations
penetrated by a borehole. Formation conductivity has been
determined based on results of measuring the magnetic field of eddy
currents that the instrument induces in the formation adjoining the
borehole. The electrical conductivity is used for, among other
reasons, inferring the fluid content of the earth formations.
Typically, lower conductivity (higher resistivity) is associated
with hydrocarbon-bearing earth formations. The physical principles
of electromagnetic induction well logging are well described, for
example, in, J. H. Moran and K. S. Kunz, Basic Theory of Induction
Logging and Application to Study of Two-Coil Sondes, Geophysics,
vol. 27, No. 6, part 1, pp. 829-858, Society of Exploration
Geophysicists, December 1962. Many improvements and modifications
to electromagnetic induction resistivity instruments described in
the Moran and Kunz reference, supra, have been devised, some of
which are described, for example, in U.S. Pat. No. 4,837,517 to
Barber, in U.S. Pat. No. 5,157,605 to Chandler et al., and in U.S.
Pat. No. 5,600,246 to Fanini et al.
The conventional geophysical induction resistivity well logging
tool is a probe suitable for lowering into the borehole and it
comprises a sensor section containing a transmitter antenna and a
receiver antenna and other, primarily electrical, equipment for
measuring data to infer the physical parameters that characterize
the formation. The sensor section, or mandrel, comprises induction
transmitters and receivers positioned along the instrument axis,
arranged in the order according to particular instrument or tool
specifications and oriented parallel with the borehole axis. The
electrical equipment generates an electrical voltage to be further
applied to a transmitter induction coil, conditions signals coming
from receiver induction coils, processes the acquired information,
stores the data or, by means of telemetry sends the data to the
earth surface through a wire line cable used to lower the tool into
the borehole.
In general, when using a conventional induction logging tool with
transmitters and receivers (induction coils) oriented only along
the borehole axis, the hydrocarbon-bearing zones are difficult to
detect when they occur in multi-layered or laminated reservoirs.
These reservoirs usually consist of thin alternating layers of
shale and sand and, oftentimes, the layers are so thin that due to
the insufficient resolution of the conventional logging tool they
cannot be detected individually. In this case the average
conductivity of the formation is evaluated.
Conventional induction well logging techniques employ coils wound
on an insulating mandrel. One or more transmitter coils are
energized by an alternating current. The oscillating magnetic field
produced by this arrangement results in the induction of currents
in the formations that are nearly proportional to the conductivity
of the formations. These currents, in turn, contribute to the
voltage induced in one or more receiver coils. By selecting only
the voltage component that is in phase with the transmitter
current, a signal is obtained that is approximately proportional to
the formation conductivity. In conventional induction logging
apparatus, the basic transmitter coil and receiver coil have axes
that are aligned with the longitudinal axis of the well logging
device. (For simplicity of explanation, it will be assumed that the
bore hole axis is aligned with the axis of the logging device, and
that these are both in the vertical direction. Also single coils
will subsequently be referred to without regard for focusing coils
or the like.) This arrangement tends to induce secondary current
loops in the formations that are concentric with the vertically
oriented transmitting and receiving coils. The resultant
conductivity measurements are indicative of the horizontal
conductivity (or resistivity) of the surrounding formations. There
are, however, various formations encountered in well logging which
have a conductivity that is anisotropic. Anisotropy results from
the manner in which formation beds were deposited by nature. For
example, "uniaxial anisotropy" is characterized by a difference
between the horizontal conductivity, in a plane parallel to the
bedding plane, and the vertical conductivity, in a direction
perpendicular to the bedding plane. When there is no bedding dip,
horizontal resistivity can be considered to be in the plane
perpendicular to the bore hole, and the vertical resistivity in the
direction parallel to the bore hole. Conventional induction logging
devices, which tend to be sensitive only to the horizontal
conductivity of the formations, do not provide a measure of
vertical conductivity or of anisotropy. Techniques have been
developed to determine formation anisotropy. See, e.g. U.S. Pat.
No. 4,302,722 to Gianzero et al. Transverse anisotropy often occurs
such that variations in resistivity occur in the azimuthal
direction.
Thus, in a vertical borehole, a conventional induction logging tool
with transmitters and receivers (induction coils) oriented only
along the borehole axis responds to the average horizontal
conductivity that combines the conductivity of both sand and shale.
These average readings are usually dominated by the relatively
higher conductivity of the shale layers and exhibit reduced
sensitivity to the lower conductivity sand layers where hydrocarbon
reserves are produced. To address this problem, loggers have turned
to using transverse induction logging tools having magnetic
transmitters and receivers (induction coils) oriented transversely
with respect to the tool longitudinal axis. Such instruments for
transverse induction well logging have been described in PCT Patent
publication WO 98/00733 of Beard et al. and U.S. Pat. No. 5,452,761
to Beard et al.; U.S. Pat. No. 5,999,883 to Gupta et al.; and U.S.
Pat. No. 5,781,436 to Forgang et al.
One, if not the main, difficulty in interpreting the data acquired
by a transversal induction logging tool is associated with
vulnerability of its response to borehole conditions. Among these
conditions is the presence of a conductive well fluid as well as
wellbore fluid invasion effects.
In the induction logging instruments, the acquired data quality
depends on the formation electromagnetic parameter distribution
(conductivity) in which the tool induction receivers operate. Thus,
in the ideal case, the logging tool measures magnetic signals
induced by eddy currents flowing in the formation. Variations in
the magnitude and phase of the eddy currents occurring in response
to variations in the formation conductivity are reflected as
respective variations in the output voltage of receivers. In the
conventional induction instruments, these receiver induction coil
voltages are conditioned and then processed using analog phase
sensitive detectors or digitized by digital-to-analog converters
and then processed with signal processing algorithms. The
processing allows for determining both receiver voltage amplitude
and phase with respect to the induction transmitter current or
magnetic field waveform. It has been found convenient for further
uphole geophysical interpretation to deliver the processed receiver
signal as a vector combination of two voltage components: one being
in-phase with transmitter waveform and another out-of-phase,
quadrature component. Theoretically, the in-phase coil voltage
component amplitude is the more sensitive and noise-free indicator
of the formation conductivity.
Recognizing the fact that no hardware calibration is perfect, and
may further be susceptible to changes over time, the present
invention provides methods for calibration of multicomponent
induction logging instruments in the presence of possible hardware
errors and misalignments.
SUMMARY OF THE INVENTION
One embodiment of the invention is a method of estimating a
parameter of interest of an earth formation. A logging tool is
conveyed into a borehole in the earth formation. Multi-component
measurements resistivity measurements are obtained using the
logging tool. The multi-component measurements are inverted without
using a particular cross-component to give a resistivity model. The
resistivity model is used to provide a simulated value of the
particular cross-component. The simulated value and the actual
value of the particular cross-component are used for estimating a
misalignment angle in the logging tool.
Another embodiment of the invention is an apparatus for estimating
a parameter of interest of an earth formation. A logging tool
obtains a plurality of multi-component resistivity measurements. A
processor inverts the multi-component measurements while excluding
a particular cross-component to give a resistivity model. The
processor then uses the resistivity model to provide a simulated
value of the particular cross-component. The processor than uses
the simulated value and the actual value of the particular
cross-component to estimate a misalignment angle in the logging
tool.
Another embodiment of the invention is a computer readable medium
for use with an apparatus for estimating a parameter of interest of
an earth formation. The apparatus includes a logging tool which
obtains a plurality of multi-component resistivity measurements.
The instructions enable a processor to invert the multi-component
measurements while excluding a particular cross-component to give a
resistivity model. The instructions further enable the processor to
use the resistivity model to provide a simulated value of the
particular cross-component. The instructions then enable the
processor to use the simulated value and the actual value of the
particular cross-component to estimate a misalignment angle in the
logging tool.
BRIEF DESCRIPTION OF THE DRAWINGS
The present invention is best understood with reference to the
accompanying figures in which like numerals refer to like elements
and in which:
FIG. 1 shows schematically a wellbore extending into a laminated
earth formation, into which wellbore an induction logging tool as
used according to the invention has been lowered;
FIG. 2A (prior art) illustrates a conventional resistivity
measurement in the vertical direction;
FIG. 2B (prior art) illustrates a resistivity measurement in the
horizontal direction;
FIG. 3 shows a borehole inclined to a bedding plane;
FIG. 4 shows a flow chart of one embodiment of the present
invention using quadrature signals;
FIG. 5 shows a flow chart of another embodiment of the present
invention using average signals; and
FIG. 6 shows a flow chart of an embodiment of the present invention
using inversion.
DETAILED DESCRIPTION OF THE INVENTION
The instrument structure provided by the present invention enables
increased stability and accuracy in an induction wellbore logging
tool and its operational capabilities, which, in turn, results in
better quality and utility of wellbore data acquired during
logging. The features of the present invention are applicable to
improve the accuracy of a transverse induction tool.
The invention will now be described in more detail, and by way of
example, with reference to the accompanying drawings. FIG. 1
schematically shows a wellbore 1 extending into a laminated earth
formation, into which wellbore an induction logging tool 9 as used
according to the present invention has been lowered. The wellbore
in FIG. 1 extends into an earth formation that includes a
hydrocarbon-bearing sand layer 3 located between an upper shale
layer 5 and a lower shale layer 7, both having higher conductivity
than the hydrocarbon bearing sand layer 3. An induction logging
tool 9 used in the practice of the invention has been lowered into
the wellbore 1 via a wireline 11 extending through a blowout
preventor 13 (shown schematically) located at the earth surface 15.
The surface equipment 22 includes an electric power supply to
provide electric power to the set of coils 18 and a signal
processor to receive and process electric signals from the receiver
coils 19. Alternatively, the power supply and/or signal processors
are located in the logging tool. It is to be noted that the term
"coil" is intended to include antennas made of non-circular
conductors as well as conductor arrangements (including rectangular
configurations) limited to a plane that are commonly used to
transmit and receive electromagnetic energy.
The relative orientation of the wellbore 1 and the logging tool 9
with respect to the layers 3, 5, 7 is determined by two angles, one
of which .theta. as shown in the FIG. 1. For determination of these
angles see, for example, U.S. Pat. No. 5,999,883 to Gupta, et al.
The logging tool 9 is provided with a set of transmitter coils 18
and a set of receiver coils 19, each set of coils 18, 19 being
connected to surface equipment 22 via suitable conductors (not
shown) extending along the wireline 11.
Each set of coils 18 and 19 includes three coils (not shown), which
are arranged such that the set has three magnetic dipole moments in
mutually orthogonal directions, that is, in x, y and z directions.
The three-coil transmitter coil set transmits T.sub.x, T.sub.y and
T.sub.z. The receiver coil receives R.sub.x, R.sub.y and R.sub.z
plus the cross-components, R.sub.xy, R.sub.xz and R.sub.zy. Thus,
coil set 18 has magnetic dipole moments 26a, 26b, 26c, and coil set
19 has magnetic dipole moments 28a, 28b, 28c. In one embodiment,
the transmitter coil set 18 is electrically isolated from the
receiver coil set 19 The apparatus and method using a wireline is
not intended to be a limitation of the invention, it being possible
to practice the invention with a logging tool on a bottomhole
assembly (BHA) conveyed on a drilling tubular. For the purposes of
the present invention, the BHA and the assembly described in FIG. 1
may be referred to as a downhole assembly.
As shown in FIG. 2A, conventional induction logging tools provide a
single transmitter coil and a receiver coil that measure
resistivity in the horizontal direction. In the conventional
horizontal mode, as shown in FIG. 2A, the resistivities of adjacent
high resistivity sand and low resistivity shale layers appear in
parallel, thus the resistivity measurement is dominated by low
resistivity shale. As shown in FIGS. 1 and 2B, in the present
invention a transverse coil is added to measure resistivity in the
vertical direction. In the vertical direction, the resistivity of
the highly resistive sand and low resistivity shale are appear in
series and thus the vertical series resistivity measurement is
dominated by the resistivity of the highly resistive sand.
For ease of reference, normal operation of the tool 9, as shown in
FIGS. 1 and 2B, will be described hereinafter only for the coils
having dipole moments in the x-direction, i.e. dipole moments 26a
and 28a. During normal operation an alternating current of a
frequency f.sub.1 is supplied by the electric power supply of
surface equipment 22 to transmitter coil set 18 so that a magnetic
field with magnetic dipole moment 26a is induced in the formation.
In an alternative embodiment, the frequency is swept through a
range f.sub.1 through f.sub.2. This magnetic field extends into the
sand layer 3 and induces a number of local eddy currents in the
sand layer 3. The magnitude of the local eddy currents is dependent
upon their location relative to the transmitter coil set 18, the
conductivity of the earth formation at each location, and the
frequency at which the transmitter coil set 18 is operating. In
principle, the local eddy currents act as a source inducing new
currents, which again induce further new currents, and so on. The
currents induced into the sand layer 3 induce a response magnetic
field in the formation, which response magnetic field is not in
phase with the transmitted magnetic field, but which induces a
response current in receiver coil set 19. The magnitude of the
current induced in the sand layer 3 depends on the conductivity of
the sand layer 3 and affects the magnitude of the response current
in receiver coil set 19. The magnitude of the response current in
receiver coil 19 also depends on the conductivity of sand layer 3
and thereby provides an indication of the conductivity of the sand
layer 3. However, the magnetic field generated by transmitter coil
set 18 not only extends into sand layer 3, but also into the
wellbore fluid and into the shale layers 5 and 7 so that currents
in the wellbore fluid and the shale layers 5 and 7 are induced.
Let us consider H.sub.XY measurement, where X is orientation of the
transmitter and Y is the orientation of the receiver. This notation
where the first subscript refers to the transmitter orientation and
the second to the receiver orientation will be used throughout the
present disclosure. We assume that if the coils are properly
aligned (exactly 90.degree. between X and Y coils) the response
from the formation will be H.sub.XYtrue. If the Y receiver is
misaligned with the X transmitter by the angle .alpha., then the
magnetic field H.sub.XY measured in such array is
H.sub.XY=H.sub.XYtruecos .alpha.+H.sub.XYtruesin .alpha. (1). The
angle .alpha. is considered to be positive if the angle between the
X and Y coils is less than 90.degree.. Those skilled in the art
having the benefit of the present disclosure would recognize that
the misalignment angle could change over time for wireline
measurements and MWD applications.
A simple example shows that even when the misalignment angle
.alpha. is small (typically 1-5.degree.) there are quite a few
cases where the misalignment error becomes comparable with the true
Hxy response. In the example, R.sub.h, the horizontal resistivity
in a direction normal to the anisotropy axis is taken as 0.5
.OMEGA.-.m; R.sub.v, the vertical resistivity (in a direction
parallel to the anisotropy axis) is taken as 2 .OMEGA.-.m; the
relative dip angle .theta. (see FIG. 3) between the tool axis and
the anisotropy axis is 20.degree.. For a relative toolface rotation
of 45.degree. and a frequency of 83.3 kHz, the true response (real
voltage converted to apparent conductivities) for the XX component
is -524.3 mS/m and for the XY component is 25.4 mS/m.
For a misalignment angle of 3.degree., the measured XY signal will
be .sigma..sub.XYmeasured=25.4 mS/mcos 3.degree.-524.3 mS/msin
3.degree.=-2.1 mS/m We can see that in this case the misalignment
error exceeds 100%, having changed by an amount of about 27.5 mS/m.
If the misalignment angle .alpha. is known, Eqn. 1 can be used for
correcting the measured XY signal. Unfortunately, the misalignment
angle .alpha. cannot be measured in advance because it can change
during pre-logging tool string assembly and also while logging due
to twisting and bending effects.
In one embodiment of the invention, the misalignment angle .alpha.
is estimated and the measurements are corrected using a
multi-frequency quadrature signal. The 3DEX tool has a 3-coil
configurations (two transmitter and one receiver coils) for
cross-components that are not mutually balanced. The main reason
for mutually balanced multi-coil arrays in induction measurements
(including main components of the 3DEX tool) is compensation of the
direct field in quadrature components. This direct field is large
compared to the formation response, so if it is not compensated and
the phase detection is not accurate enough, it will propagate in
the real voltage and cause undesired distortion. For
cross-components measurements, the mutual balancing is not as
important because the direct field of the X transmitter does not
contribute into the Y receiver due to orthogonality. But if the X
and Y coils are misaligned, the direct field from unbalanced X
transmitters does contribute to the Y quadrature signal. The
misalignment angle .alpha. is estimated based on the amplitude of
this signal.
Eqn. (1) is used to analyze the misaligned XY quadrature signal.
The response consists of the cosine projection of true XY formation
quadrature signal and the sine projection of true XX signal. The
true XX signal is dominated by the direct field, which is frequency
and formation independent. If we extract the constant part of the
XY quadrature signal and compare it with the total direct field, we
will be able to find the misalignment angle. For example, let us
consider the 3DEX response in the following model: R.sub.h=1
.OMEGA.-m; R.sub.v=4 .OMEGA.-m; Relative dip=45.degree.; Relative
rotation=45.degree.; Frequency=20.83 kHz. The values of the XY
quadrature formation response and the direct field for a 2.degree.
misalignment for this model are presented in Table 1. It can be
seen that in this case the formation response is comparable with
the direct field, meaning that we have to separate the direct field
from the formation response to accurately estimate the misalignment
angle.
TABLE-US-00001 TABLE 1 Comparison of the XY formation response and
the direct field caused by 2.degree. misalignment Direct field for
2.degree. Formation relative XY formation response misalignment
contribution Re(Hxy) (Wb/m.sup.2) (Wb/m.sup.2) % 0.0474 * 10.sup.-3
-0.0903 * 10.sup.-3 52.5
The separation of the direct field from the formation response in
the quadrature signal may be achieved by applying the Taylor
expansion used in multi-frequency focusing of the real signal.
Using results from U.S. Pat. No. 5,884,227 to Rabinovich et al.,
the quadrature signal is given by the Taylor series expansion:
Re(H)=b.sub.0+b.sub.1.omega..sup.3/2+b.sub.2.omega..sup.2+b.sub.3.omega..-
sup.5/2+b.sub.4.omega..sup.7/2+b.sub.5.omega..sup.4+b.sub.6.omega..sup.9/2
(2) The first term in this expansion is independent of frequency
and represents the direct field. In the present invention,
multi-frequency quadrature measurements are made and this first
term is extracted using the Taylor series expansion. Typically,
this is done using a multi-frequency focusing algorithm with the
appropriate power series. To test our invention, we generated
synthetic data for two different models: 1. R.sub.h=10 .OMEGA.-m;
R.sub.v=40 .OMEGA.-m, Relative dip=45.degree., Relative
rotation=45.degree.; 2. R.sub.h=1 .OMEGA.-m; R.sub.v=4 .OMEGA.-m,
Relative dip=45.degree., Relative rotation=45.degree.. For each
model we calculated responses for 5 different misalignment angles:
0, 1, 2, 3, 4, 5 degrees. The term "misalignment angle" when used
with respect to coils that are nominally orthogonal to each other
means a difference from 90.degree. in alignment. For each
misalignment angle we applied the above-described procedure to
extract the direct field from the data, and based on this value,
calculated the misalignment angle. The results for the both models
are presented in the tables below.
TABLE-US-00002 TABLE 2 Calculation of the misalignment angle for
the Model 1. Extracted direct Calculated True misalignment field
Total direct field misalignment angle (deg) (Wb/m.sup.2)
(Wb/m.sup.2) angle (deg) 5 -0.225 * 10.sup.-3 -0.2586 * 10.sup.-2
4.99 4 -0.180 * 10.sup.-3 -0.2586 * 10.sup.-2 3.99 3 -0.135 *
10.sup.-3 -0.2586 * 10.sup.-2 2.99 2 -0.902 * 10.sup.-4 -0.2586 *
10.sup.-2 1.999 1 -0.451 * 10.sup.-4 -0.2586 * 10.sup.-2 0.999 0
-0.450 * 10.sup.-6 -0.2586 * 10.sup.-2 0.01
TABLE-US-00003 TABLE 3 Calculation of the misalignment angle for
the Model 2. Extracted direct Total Calculated True misalignment
field direct field misalignment angle (deg) (Wb/m.sup.2)
(Wb/m.sup.2) angle (deg) 5 -0.224 * 10.sup.-3 -0.2586 * 10.sup.-2
4.97 4 -0.179 * 10.sup.-3 -0.2586 * 10.sup.-2 3.97 3 -0.134 *
10.sup.-3 -0.2586 * 10.sup.-2 2.97 2 -0.885 * 10.sup.-4 -0.2586 *
10.sup.-2 1.96 1 -0.433 * 10.sup.-4 -0.2586 * 10.sup.-2 0.96 0
-0.188 * 10.sup.-5 -0.2586 * 10.sup.-2 0.04
This embodiment of the invention may be represented by the flow
chart of FIG. 4. Data are acquired at a plurality of frequencies
101. As a specific example, the transmitter is an X transmitter and
the receiver is a Y receiver. A multi-frequency focusing of the
quadrature magnetic signal is performed 103 using eqn. (2) to give
the direct field between the transmitter and the receiver. This may
also be done using an equivalent formulation for the electric field
using methods known to those versed in the art having the benefit
of the present disclosure. Using the estimated direct field, the
misalignment angle is estimated 105. The estimated misalignment
angle may then be used to correct the individual single frequency
measurements, including the in-phase components 107. It should be
noted that while the description above has been made with respect
to the XY component, from reciprocity considerations, the method is
equally valid for the YX component.
Once the misalignment angle is estimated, all of the
multi-component signals can be corrected for misalignment and used
for interpreting formation resistivities and petrophysical
parameters. The principles used for this interpretation have been
discussed, for example, in U.S. Pat. No. 6,470,274 to Mollison et
al, U.S. Pat. No. 6,643,589 to Zhang et al., U.S. Pat. No.
6,636,045 to Tabarovsky et al., the contents of which are
incorporated herein by reference. Specifically, the parameters
estimated may include horizontal and vertical resistivities (or
conductivities), relative dip angles, strike angles, sand and shale
content, and water saturation.
The method described above is generally not applicable when a
co-located transmitter coil array is used in conjunction with a
co-located main receiver coil array and a co-located bucking
receiver coil array. In such a situation, the main and bucking
coils are decoupled and the misalignment is estimated separately
for the main and bucking coils.
A second embodiment of the invention is based on recognition of the
fact that for a given anisotropic formation with a particular
relative dip, the XY cross-component response will change from a
negative value at -45.degree. relative rotation to a positive value
of equal magnitude at 45.degree. relative rotation. A zero-crossing
will occur at 0.degree. relative rotation. The actual magnitude of
the positive and negative values will be dependent on the
resistivity and the relative dip properties of the formation, but
the response should always oscillate about zero for a perfectly
aligned tool rotating in a uniform anisotropic formation.
If the X transmitters and the Y receiver are misaligned, a portion
of the direct XX signal will be introduced into the XY response as
described previously. If the tool is rotating through a uniform
formation, the deviation of the oscillations away from zero allows
this misalignment to be computed.
To apply the technique, a relatively uniform formation (typically a
thick shale interval) is chosen for making measurements with the
3DEX tool. The tool is rotated within the borehole. For wireline
applications, this may require an auxiliary motor for rotating the
tool or may result from rotation of the wireline and the downhole
assembly as it is conveyed through the borehole. For
measurement-while-drilling (MWD) applications, the rotation is
accomplished by the rotation of the bottomhole assembly (BHA) that
carries the 3DEX tool. The average XY and XX responses across this
formation are computed. Based on the eqn. (1) and the assumption
that the average H.sub.XYtrue should be zero, where the overbar
represents an averaging, the misalignment angle may be computed
using average responses. H.sub.XY=H.sub.XXtruesin .alpha. (3) This
technique assumes that the misalignment is not changing and will
not compensate for twisting and bending while logging unless the
effect remains consistent. The estimation of bias in ZX
measurements on a rotating drillstring has been discussed in U.S.
patent application Ser. No. 11/299,053 of Chemali et al, having the
same assignee as the present invention and the contents of which
are incorporated herein by reference. Once the misalignment angle
has been estimated, measurements may be corrected using eqn.
(1).
The flow chart for this method is illustrated in FIG. 5. The tool
is lowered into a substantially homogenous interval 201. The
H.sub.xx and H.sub.xy measurements are made at a plurality of
rotational angles as the tool rotates 203. The H.sub.xy
measurements correspond to measurements made with a first receiver
antenna and the H.sub.xx measurements corresponds to measurements
made with a second receiver antenna. The measurements are averaged
and the misalignment angle estimated 205. In one embodiment of the
invention, the measurements are made at uniformly spaced angles and
a simple averaging can be done. In another embodiment of the
invention, the measurements may be made with non-uniform rotational
angles and an appropriate averaging procedure may be used. The
estimated bias provides and estimate of the misalignment angle may
then be used to correct the measurements 207 made in other portions
of the wellbore using eqn. (1) and a parameter of interest of the
earth formation estimated.
Another embodiment of the present invention uses an inversion of
3DEX data to obtain horizontal resistivity, vertical resistivity,
and formation dip and azimuth, and requires the use of
multi-component measurements including the three primary components
(XX,YY,ZZ) plus at least one cross-component (XY or XZ). A method
for simultaneous determination of formation angles and anisotropic
resistivity using multi-component induction logging data is
disclosed in U.S. Pat. No. 6,643,589 to Zhang et al., having the
same assignee as the present invention and the contents of which
are incorporated herein by reference. The inversion is performed
using a gradient technique such as a generalized
Marquardt-Levenberg method. In this generalized Marquardt-Levenberg
method, a data objective function is defined that is related to a
difference between the model output and the measured data. The
iterative procedure involves reducing a global objective function
that is the sum of the data objective function and a model
objective function related to changes in the model in successive
iterations. In an alternate embodiment of the invention, the
formation azimuth angle is excluded from the iterative process by
using derived relations between the multicomponent measurements.
The gradient technique is part of a class of techniques
collectively referred to as search techniques.
When multi-array induction measurements are also available, an
inversion method is described in U.S. Pat. No. 6,885,947 to Xiao et
al., having the same assignee as the present invention and the
contents of which are incorporated herein by reference. Data are
acquired using a multi-array logging tool in a borehole having an
angle of inclination to a normal to the bedding plane of earth
formations. The multi-array measurements are filtered using angle
dependent filters to give a filtered curve corresponding to a
target one of the multi-array measurements using angle-dependent
filters. Correlation coefficients are estimated for a set of
possible dip angles and a relative dip angle is estimated from the
correlation coefficients. This dip angle estimate together with bed
boundaries obtained from the multi-array measurements are used for
inverting multi-component measurements alone or jointly with
multi-array measurements to refine the relative dip angle
interpretation and give horizontal and vertical formation
resistivity.
Yet another inversion method using a separation of modes is
disclosed in U.S. Pat. No. 6,636,045 to Tabarovsky et al having the
same assignee as the present invention and the contents of which
are incorporated herein by reference. In Tabarovsky, a combination
of principal component measurements is used to estimate the
horizontal resistivity of the earth formations. The estimated
horizontal resistivities are used in a model for inversion of other
components of the data to obtain the vertical formations
resistivities. Tabarovsky further uses multifrequency focusing when
multifrequency measurements are available.
Another inversion method is described in U.S. patent application
Ser. No. 10/867,619 of Tabarovsky et al, having the same assignee
as the present invention and the contents of which are incorporated
herein by reference. In one embodiment of the Tabarovsky '619,
using known values of the relative dip angle and azimuth, the
focused measurements are separated into two or more fundamental
modes. One of the fundamental modes is related primarily to the
horizontal conductivity (or resistivity) of the earth formation, so
that the horizontal conductivity may be obtained from the first
mode. Using the estimated horizontal conductivity and the second
mode, the vertical conductivity may be estimated. In another
embodiment of the invention, the fundamental modes and the relative
dip angle and azimuth are estimated simultaneously using
measurements made at a plurality of depths. The simultaneous
determination is done by searching over a range of relative dip
angles and azimuths. Alternatively, the search may be done over a
range of absolute dips and azimuths and using measurements made by
orientation and navigation sensors on the tool.
One embodiment of the present invention uses an inversion technique
such as that described in Zhang et al., Xiao et al., Tabarovsky et
al., or any other suitable inversion method. A common
characteristic of all of the methods is that a more stable and
unique solution for formation dip and azimuth is estimated when
both cross-components are included. However, if the
cross-components are perfectly aligned, the same solution for
formation dip and azimuth should be achieved if either the XY or
the XZ components are omitted. If the XY component is in error due
to misalignment, this will not be true.
The inversion technique to check for misalignment initially inverts
the data with a particular cross-component such as the XY component
omitted. Forward modeling is then used with these results to
generate a simulated (expected) XY response. The average difference
between the simulated and actual XY responses should be zero. Any
difference is attributed to misalignment.
To apply the technique, the average XX and XY responses are
estimated over the entire logging interval along with the average
simulated XY response obtained by forward modeling from the
inversion performed without the XY measurement. Based on the eqn.
(1) and the assumption that the simulated XY response represents
H.sub.XYtrue, the misalignment angle may be computed using average
responses. H.sub.xy.sup.measured- H.sub.xy.sup.simulated= H.sub.xx
sin .alpha. where the overbar represents and averaging. This
technique also assumes that the misalignment is not changing and
will not compensate for twisting and bending while logging unless
the effect remains consistent. Once the correction is estimated and
applied, a new inversion of the multi-component measurements may be
carried out using all the available components.
FIG. 6 is a flow chart of this method. Multicomponent measurements
(optionally with multiarray measurements) are acquired and the
measurements are inverted without using the XY component 301.
Simulated XY measurements are generated for the model 305. The XX
and XY measurements are averaged over the interval 305. Next, the
misalignment angles is estimated 307 as discussed above.
Implicit in the control and processing of the data is the use of a
computer program on a suitable machine-readable medium that enables
the processor to perform the control and processing. The
machine-readable medium may include ROMs, EPROMs, EAROMs, Flash
Memories and Optical disks.
While the foregoing disclosure is directed to the preferred
embodiments of the invention, various modifications will be
apparent to those skilled in the art. It is intended that all
variations within the scope and spirit of the appended claims be
embraced by the foregoing disclosure.
The following definitions are helpful in understanding the scope of
the invention: alignment: the proper positioning or state of
adjustment of parts in relation to each other; calibrate: to
standardize by determining the deviation from a standard so as to
ascertain the proper correction factors; coil: one or more turns,
possibly circular or cylindrical, of a current-carrying conductor
capable of producing a magnetic field; EAROM: electrically
alterable ROM; EPROM: erasable programmable ROM; flash memory: a
nonvolatile memory that is rewritable; machin-readable medium:
something on which information may be stored in a form that can be
understood by a computer or a processor; misalignment: the
condition of being out of line or improperly adjusted; for the
cross-component, this is measured by a deviation from
orthogonality; Optical disk: a disc-shaped medium in which optical
methods are used for storing and retrieving information; Position:
an act of placing or arranging; the point or area occupied by a
physical object Quadrature: 90.degree. out of phase; and ROM:
Read-only memory.
* * * * *